First, the theoretical performance difference; the second is the difference browser compatibility.
Performance differences:
[border: 0;} The border is set to "0" pixel though invisible on the page, but defaults by border understanding, the browser is still on the border-width / border-color has been rendered, that is already occupied memory value.
[Border: none;} The border is set to "none" that is not, will not make the browser render action to resolve "none", that is, not consumed memory value.
Compatibility differences: differences only for compatibility with the browser IE6, IE7 and tag button, input, it will appear in this case under XP theme win, win7, vista's. [Border: none;} When the border is "none" seems to IE6 / 7 invalid border still exists,